David Bryant posted this puzzle in a different topic in this forum, but that string is getting so long I thought I'd post a new topic for comments (and I finally got a chance to look at it). I am new to this, so forgive my inaccurate lexicon:

Now I throw up my hands. It's like a perfect storm of perfectly matched candidates. By that I mean that the puzzle has not been solved for the 1247 and 9, but no cell has a "stray candidate" (one that dosen't match itself in its row, column, or box) -- or, put another way, there is no logical way to "guess" where you might start an x-z wing or a set for forcing chains.

So this is how I solved the puzzle (but what I really want to know is what is the "right" way to solve the puzzle, because whatever the definition of "trial and error" is, I think this really pushes the envelope):

There are a slew of cells with 7 as a candidate -- 20 to be exact. There are six "pairs" where only two 7s can fit in a column, row, or box. So the odds that there is some coloring going on are pretty high, and this "method" (I use the term losely) only takes two minutes.

If you look at that (I drew arrows on the grid) you see that there is only one 7 that is linked twice and only one "box only" connection -- an "imbalance"? -- and both are in the center of the puzzle. That leads me to believe (based on my experience in with x-y wings and forcing chains) that there is hope for this attempt. But you can immediately see that r5c5=7 gets you nowhere.

So I decide, based on a gut assessment of the pattern, that r1c1 is the place to start. From there it is easy to determine the if r1c1=7, r5c5= not 7 (or r5c3=7); and if r1c1= not 7, r5c5 = not 7 (or r5c3=7).

So now I have solved two cells (r5c3 and r6c6), and the puzzle crumbles.

BTW -- to test this puzzle (for kicks) I plugged in the numbers from where I stalled (second from the top) into the draw program, and it said "Unsolv able..." I added the 7 at r5c3, and the program said "Easy."